Problem: Express your answer as a mixed number simplified to lowest terms. $4\dfrac{2}{6}-2\dfrac{4}{5} = {?}$
Simplify each fraction. $= {4\dfrac{1}{3}} - {2\dfrac{4}{5}}$ Find a common denominator for the fractions: $= {4\dfrac{5}{15}}-{2\dfrac{12}{15}}$ Convert ${4\dfrac{5}{15}}$ to ${3 + \dfrac{15}{15} + \dfrac{5}{15}}$ So the problem becomes: ${3\dfrac{20}{15}}-{2\dfrac{12}{15}}$ Separate the whole numbers from the fractional parts: $= {3} + {\dfrac{20}{15}} - {2} - {\dfrac{12}{15}}$ Bring the whole numbers together and the fractions together: $= {3} - {2} + {\dfrac{20}{15}} - {\dfrac{12}{15}}$ Subtract the whole numbers: $=1 + {\dfrac{20}{15}} - {\dfrac{12}{15}}$ Subtract the fractions: $= 1+\dfrac{8}{15}$ Combine the whole and fractional parts into a mixed number: $= 1\dfrac{8}{15}$